Properties

Label 6018.2.a.l
Level 6018
Weight 2
Character orbit 6018.a
Self dual Yes
Analytic conductor 48.054
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0539719364\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} + 2q^{5} + q^{6} - 4q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} + q^{3} + q^{4} + 2q^{5} + q^{6} - 4q^{7} + q^{8} + q^{9} + 2q^{10} + 4q^{11} + q^{12} - 2q^{13} - 4q^{14} + 2q^{15} + q^{16} + q^{17} + q^{18} - 4q^{19} + 2q^{20} - 4q^{21} + 4q^{22} + 4q^{23} + q^{24} - q^{25} - 2q^{26} + q^{27} - 4q^{28} + 10q^{29} + 2q^{30} + 4q^{31} + q^{32} + 4q^{33} + q^{34} - 8q^{35} + q^{36} + 2q^{37} - 4q^{38} - 2q^{39} + 2q^{40} - 6q^{41} - 4q^{42} + 12q^{43} + 4q^{44} + 2q^{45} + 4q^{46} - 8q^{47} + q^{48} + 9q^{49} - q^{50} + q^{51} - 2q^{52} + 6q^{53} + q^{54} + 8q^{55} - 4q^{56} - 4q^{57} + 10q^{58} - q^{59} + 2q^{60} + 10q^{61} + 4q^{62} - 4q^{63} + q^{64} - 4q^{65} + 4q^{66} - 4q^{67} + q^{68} + 4q^{69} - 8q^{70} - 12q^{71} + q^{72} + 10q^{73} + 2q^{74} - q^{75} - 4q^{76} - 16q^{77} - 2q^{78} + 12q^{79} + 2q^{80} + q^{81} - 6q^{82} + 12q^{83} - 4q^{84} + 2q^{85} + 12q^{86} + 10q^{87} + 4q^{88} + 10q^{89} + 2q^{90} + 8q^{91} + 4q^{92} + 4q^{93} - 8q^{94} - 8q^{95} + q^{96} + 10q^{97} + 9q^{98} + 4q^{99} + O(q^{100}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
0
1.00000 1.00000 1.00000 2.00000 1.00000 −4.00000 1.00000 1.00000 2.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(17\) \(-1\)
\(59\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6018))\):

\( T_{5} - 2 \)
\( T_{7} + 4 \)